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Research

My current research focuses on set theory with urelements. I am interested in reflection principles, choice principles, forcing, and large cardinals in the presence of urelements. I also have interests in potentialism, abstraction principles, and the relationship between mereology and set theory.

 

Papers

  1.  Axiomatization and Forcing in Set Theory with Urelements. Journal of Symbolic Logic. Journal Arxiv 

  2. Boolean-valued Models of Set Theory with Urelements, with Xinhe Wu. Notre Dame Journal of Formal Logic. 65 (2):203-227. 2024. Journal PDF         

  3. Reflective Mereology. Journal of Philosophical Logic 52 (4): 1171-1196. 2023. Journal PDF

  4. Reflection in Second-Order Set Theory with Abundant Urelements Bi-Interprets a Supercompact Cardinal, with Joel David Hamkins. Journal of Symbolic Logic:1-36. 2022. Journal Arxiv   

  5. Reflection Principles and Second-Order Choice Principles with Urelements. Annals of Pure and Applied Logic 173 (4):103073. 2022. Journal

  6. Ability and the Past. American Philosophical Quarterly 56 (4):397-406. 2019. Journal

  7. Abstraction Principles and Size of Reality. Submitted. PDF

 

Dissertation

       Set Theory with Urelements. Arxiv

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